Quantum Fidelity Estimation in the Resource Theory of Nonstabilizerness

TL;DR

This paper introduces efficient fidelity estimation protocols for quantum states and channels in the resource theory of nonstabilizerness, linking their complexity to measures like mana and Wigner rank, with implications for quantum benchmarking.

Contribution

It proposes novel fidelity estimation methods requiring minimal measurements, and connects their sample complexity to nonstabilizerness measures, providing operational insights.

Findings

Protocols require constant expectation value measurements.

Sample complexity scales with nonstabilizerness measures.

Fidelity estimation is tractable for states with efficient classical simulation.

Abstract

Quantum fidelity estimation is essential for benchmarking quantum states and processes on noisy quantum devices. While stabilizer operations form the foundation of fault-tolerant quantum computing, non-stabilizer resources further enable universal quantum computation through state injection. In this work, we propose several efficient fidelity estimation protocols for both quantum states and channels within the resource theory of nonstabilizerness, focusing on qudit systems with odd prime dimensions. Our protocols require measuring only a constant number of phase-space point operator expectation values, with operators selected randomly according to an importance weighting scheme tailored to the target state. Notably, we demonstrate that mathematically defined nonstabilizerness measures--such as Wigner rank and mana--quantify the sample complexity of the proposed protocols, thereby endowing them with a clear operational interpretation in the fidelity estimation task. This connection reveals a fundamental trade-off: while fidelity estimation for general quantum states and channels requires resources that scale exponentially with their nonstabilizerness, the task remains tractable for states and channels that admit efficient classical simulation.